{% extends 'homepage.html' %}
{% block content %}

<p>
  A
  <a class="knowl-title" knowl="smf.siegel_modular_form">
    Siegel modular form
  </a>
  of degree 2 is a holomorphic function on the Siegel upper half plane of complex two by two matrices
  whose imaginary part is strictly positive definite which satisfies an invariance property with respect to
  arithmetic subgroups of <script type="math/tex">{\rm GSp}(4)</script> such as the ones listed below.
</p>

<br/>

<h2>Browse</h2>

<p>
  Integral weight by group:
  &nbsp;&nbsp;
  <a href="{{ url_for( 'ModularForm_GSp4_Q_top_level', group = 'Sp4Z', page = 'forms') }}">
    <script type="math/tex">{\rm Sp}(4,\mathbb{Z})</script>
  </a>
  &nbsp;&nbsp;
  <a href="{{ url_for( 'ModularForm_GSp4_Q_top_level', group = 'Kp', page = 'forms') }}">
    <script type="math/tex">K(p)</script>
  </a>
  &nbsp;&nbsp;
  <a href="{{ url_for( 'ModularForm_GSp4_Q_top_level', group = 'Gamma0_2', page = 'forms') }}">
    <script type="math/tex">\Gamma_0(2)</script>
  </a>
  &nbsp;&nbsp;
  <a href="{{ url_for( 'ModularForm_GSp4_Q_top_level', group = 'Gamma0_3_psi_3', page = 'forms') }}">
    <script type="math/tex">\Gamma_0(3),\psi_3</script>
  </a>
  &nbsp;&nbsp;
  <a href="{{ url_for( 'ModularForm_GSp4_Q_top_level', group = 'Gamma0_4_psi_4', page = 'forms') }}">
    <script type="math/tex">\Gamma_0(4),\psi_4</script>
  </a>
</p>

<p>
  Half integral weight by group:
  &nbsp;&nbsp;
  <a href="{{ url_for( 'ModularForm_GSp4_Q_top_level', group = 'Gamma0_4_', page = 'forms') }}">
    <script type="math/tex">\Gamma_0(4),\left(\frac{-4}{*}\right)</script>
  </a>
</p>

<p>
  <script type="math/tex">\mathbb{C}[X,Y]</script>-valued and integral weight by group:
  &nbsp;&nbsp;
  <a href="{{ url_for( 'ModularForm_GSp4_Q_top_level', group = 'Sp4Z_2', page = 'forms') }}">
    <script type="math/tex">{\rm Sp}(4,\mathbb{Z})</script>
  </a>
</p>

<br/>

<h2>Look up dimensions</h2>

<br/>

<h2>Search</h2>

<p>
  <form action="/LfunctionDB/query" method=get> 
    <table> 
      <tr> 
	<td>Group and character</td>
	<td>
	  <select>
	    <option><script type="math/tex">{\rm Sp}(4,\mathbb{Z})</script></option>
	    <option><script type="math/tex">K(p)</script></option>
	    <option><script type="math/tex">\Gamma_0(2)</script></option>
	    <option><script type="math/tex">\Gamma_0(3),\psi_3</script></option>
	    <option><script type="math/tex">\Gamma_0(4),\psi_4</script></option>
	    <option><script type="math/tex">\Gamma_0(4),\left(\frac{-4}{*}\right)\</script></option>
	  </select>
	</td>
      </tr>

      <tr> 
	<td>Weight</td><td> <input type='text' name='weight' size = '4'></td><td><span class="formexample"> e.g. 2 or 3/2 or 2,1</span></td> 
      </tr> 
      
      <tr> 
	<td> 
	  <button type='submit' name='search' value='Search'/> 
	</td> 
      </tr> 
    </table> 
  </form> 
</p>

{% endblock %}
